Getting a bit mathematical now. When pricing an option, we are attempting to put a value on the probability of future price movements. So we are now terribly interested in the mean and standard deviation of an underlyings price movements.
The mean is the average price movement, whilst the standard deviation tells us how far the price moved. Using these figures (& volatility which is a measure of how fast the price is expected to move), we can model the distribution of expected price movements.
Of course, expected is not the same thing as actual; which always makes things a bit more interesting.
Next up, the Black Scholes model.